Large, multi-dimensional, numerical arrays.
This module implements multi-dimensional arrays of integers and floating-point numbers, thereafter referred to as 'Bigarrays', to distinguish them from the standard OCaml arrays described in
The implementation allows efficient sharing of large numerical arrays between OCaml code and C or Fortran numerical libraries.
The main differences between 'Bigarrays' and standard OCaml arrays are as follows:
- Bigarrays are not limited in size, unlike OCaml arrays. (Normal float arrays are limited to 2,097,151 elements on a 32-bit platform, and normal arrays of other types to 4,194,303 elements.)
- Bigarrays are multi-dimensional. Any number of dimensions between 0 and 16 is supported. In contrast, OCaml arrays are mono-dimensional and require encoding multi-dimensional arrays as arrays of arrays.
- Bigarrays can only contain integers and floating-point numbers, while OCaml arrays can contain arbitrary OCaml data types.
- Bigarrays provide more space-efficient storage of integer and floating-point elements than normal OCaml arrays, in particular because they support 'small' types such as single-precision floats and 8 and 16-bit integers, in addition to the standard OCaml types of double-precision floats and 32 and 64-bit integers.
- The memory layout of Bigarrays is entirely compatible with that of arrays in C and Fortran, allowing large arrays to be passed back and forth between OCaml code and C / Fortran code with no data copying at all.
- Bigarrays support interesting high-level operations that normal arrays do not provide efficiently, such as extracting sub-arrays and 'slicing' a multi-dimensional array along certain dimensions, all without any copying.
Users of this module are encouraged to do
open Bigarray in their source, then refer to array types and operations via short dot notation, e.g.
Bigarrays support all the OCaml ad-hoc polymorphic operations:
- comparisons (
<=, etc, as well as
- hashing (module
- and structured input-output (the functions from the
Marshalmodule, as well as
Bigarrays can contain elements of the following kinds:
- IEEE single precision (32 bits) floating-point numbers (
- IEEE double precision (64 bits) floating-point numbers (
- IEEE single precision (2 * 32 bits) floating-point complex numbers (
- IEEE double precision (2 * 64 bits) floating-point complex numbers (
- 8-bit integers (signed or unsigned) (
- 16-bit integers (signed or unsigned) (
- OCaml integers (signed, 31 bits on 32-bit architectures, 63 bits on 64-bit architectures) (
- 32-bit signed integers (
- 64-bit signed integers (
- platform-native signed integers (32 bits on 32-bit architectures, 64 bits on 64-bit architectures) (
Each element kind is represented at the type level by one of the
*_elt types defined below (defined with a single constructor instead of abstract types for technical injectivity reasons).
- since 4.07.0 Moved from otherlibs to stdlib.
type ('a, 'b) kind =
| Float32 : (float, float32_elt) kind
| Float64 : (float, float64_elt) kind
| Int8_signed : (int, int8_signed_elt) kind
| Int8_unsigned : (int, int8_unsigned_elt) kind
| Int16_signed : (int, int16_signed_elt) kind
| Int16_unsigned : (int, int16_unsigned_elt) kind
| Int32 : (int32, int32_elt) kind
| Int64 : (int64, int64_elt) kind
| Int : (int, int_elt) kind
| Nativeint : (nativeint, nativeint_elt) kind
| Complex32 : (Complex.t, complex32_elt) kind
| Complex64 : (Complex.t, complex64_elt) kind
| Char : (char, int8_unsigned_elt) kind
To each element kind is associated an OCaml type, which is the type of OCaml values that can be stored in the Bigarray or read back from it. This type is not necessarily the same as the type of the array elements proper: for instance, a Bigarray whose elements are of kind
float32_elt contains 32-bit single precision floats, but reading or writing one of its elements from OCaml uses the OCaml type
float, which is 64-bit double precision floats.
The GADT type
('a, 'b) kind captures this association of an OCaml type
'a for values read or written in the Bigarray, and of an element kind
'b which represents the actual contents of the Bigarray. Its constructors list all possible associations of OCaml types with element kinds, and are re-exported below for backward-compatibility reasons.
Using a generalized algebraic datatype (GADT) here allows writing well-typed polymorphic functions whose return type depend on the argument type, such as:
let zero : type a b. (a, b) kind -> a = function | Float32 -> 0.0 | Complex32 -> Complex.zero | Float64 -> 0.0 | Complex64 -> Complex.zero | Int8_signed -> 0 | Int8_unsigned -> 0 | Int16_signed -> 0 | Int16_unsigned -> 0 | Int32 -> 0l | Int64 -> 0L | Int -> 0 | Nativeint -> 0n | Char -> '\000'
As shown by the types of the values above, Bigarrays of kind
float64_elt are accessed using the OCaml type
float. Bigarrays of complex kinds
complex64_elt are accessed with the OCaml type
Complex.t. Bigarrays of integer kinds are accessed using the smallest OCaml integer type large enough to represent the array elements:
int for 8- and 16-bit integer Bigarrays, as well as OCaml-integer Bigarrays;
int32 for 32-bit integer Bigarrays;
int64 for 64-bit integer Bigarrays; and
nativeint for platform-native integer Bigarrays. Finally, Bigarrays of kind
int8_unsigned_elt can also be accessed as arrays of characters instead of arrays of small integers, by using the kind value
char instead of
val kind_size_in_bytes : ('a, 'b) kind -> int
kind_size_in_bytes k is the number of bytes used to store an element of type
- since 4.03.0
To facilitate interoperability with existing C and Fortran code, this library supports two different memory layouts for Bigarrays, one compatible with the C conventions, the other compatible with the Fortran conventions.
In the C-style layout, array indices start at 0, and multi-dimensional arrays are laid out in row-major format. That is, for a two-dimensional array, all elements of row 0 are contiguous in memory, followed by all elements of row 1, etc. In other terms, the array elements at
(x, y+1) are adjacent in memory.
In the Fortran-style layout, array indices start at 1, and multi-dimensional arrays are laid out in column-major format. That is, for a two-dimensional array, all elements of column 0 are contiguous in memory, followed by all elements of column 1, etc. In other terms, the array elements at
(x+1, y) are adjacent in memory.
The GADT type
'a layout represents one of the two supported memory layouts: C-style or Fortran-style. Its constructors are re-exported as values below for backward-compatibility reasons.
module Genarray : sig ... end
module Array0 : sig ... end
Zero-dimensional arrays. The
Array0 structure provides operations similar to those of
Bigarray.Genarray, but specialized to the case of zero-dimensional arrays that only contain a single scalar value. Statically knowing the number of dimensions of the array allows faster operations, and more precise static type-checking.
module Array1 : sig ... end
One-dimensional arrays. The
Array1 structure provides operations similar to those of
Bigarray.Genarray, but specialized to the case of one-dimensional arrays. (The
Array3 structures below provide operations specialized for two- and three-dimensional arrays.) Statically knowing the number of dimensions of the array allows faster operations, and more precise static type-checking.
module Array2 : sig ... end
Two-dimensional arrays. The
Array2 structure provides operations similar to those of
Bigarray.Genarray, but specialized to the case of two-dimensional arrays.
module Array3 : sig ... end
Three-dimensional arrays. The
Array3 structure provides operations similar to those of
Bigarray.Genarray, but specialized to the case of three-dimensional arrays.